Stats 300B: Theory of Statistics II
Course Schedule (subject to change)
| Lecture Notes | Topics | Reading |
| Tue, Jan 12 | Lecture 1 | Overview, Convergence of random variables | VDV Chapters 2.1, 2.2 |
| Thu, Jan 14 | Lecture 2 | Convergence of random variables, delta method | VDV Chapters 2, 3 |
| Tue, Jan 19 | Lecture 3 | Asymptotic normality, Fisher information | VDV Chapter 5.1-5.6; ELST Chapter 7.1-7.3 |
| Thu, Jan 21 | Lecture 4 | Fisher information, Moment method | VDV Chapter 4; TPE Chapter 2.5 |
| Tue, Jan 26 | Lecture 5 | Superefficiency, Testing and Confidence Regions | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Thu, Jan 28 | Lecture 6 | Testing: likelihood ratio, Wald, Score tests | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Tue, Feb 2 | Lecture 7 | U-Statistics | VDV Chapter 12 |
| Thu, Feb 4 | Lecture 8 | U-Statistics: Hajek projections and asymptotic normality | VDV Chapter 11, 12 |
| Tue, Feb 9 | Lecture 9 | Uniform laws of large numbers, Covering and Bracketing | VDV Chapter 5.2, 19.1, 19.2 |
| Thu, Feb 11 | Lecture 10 | Subgaussianity, Symmetrization, Rademacher complexity and metric entropy | VDV Chapter 19, HDP Chapter 1, 2, 8 |
| Tue, Feb 16 | Lecture 11 | Symmetrization, Chaining | HDP Chapter 8, VDV Chapter 18-19 |
| Thu, Feb 18 | Lecture 12 | Uniform laws via entropy numbers, classes with finite entropy, VC classes | VDV Chapter 18-19 |
| Tue, Feb 23 | Lecture 13 | Rademacher complexity and ULLNs | VDV Chapter 18-19 |
| Thu, Feb 25 | Lecture 14 | Moduli of continuity, rates of convergence | VDV Chapter 18-19 |
| Tue, Mar 2 | Lecture 15 | Weak convergence of random functions | VDV Chapter 18-19, Notes on Arzela-Ascoli theorem |
| Thu, Mar 4 | Lecture 16 | Goodness-of-fit tests, M-estimators with non-differentiable losses | VDV Chapter 19.3 & 5.3 |
| Tue, Mar 9 | | Quadratic mean differentiability | TSH Chapter 12, VDV Chapter 6 |
| Thu, Mar 11 | Lecture 18 | Absolute continuity of measure, Contiguity, LeCams's lemmas, Distance for distributions | TSH Chapter 12.3, VDV Chapter 6 |
| Tue, Mar 16 | Lecture 19 | Hellinger distance, Quadratic mean differentiability, Local asymptotic normality, Asymptotically most powerful tests | TSH Chapter 12.3, 13.1-13.3, VDV Chapter 6, 7.1-7.3 |
| Thu, Mar 18 | Lecture 20 | Limiting Gaussian experiments, Local asymptotic minimax theorem | VDV Chapters 7 and 8, Notes on class website
|
VDV = van der Vaart (Asymptotic Statistics)
HDS = Wainwright (High Dimensional Statistics: A Non-Asymptotic Viewpoint)
HDP = Vershynin (High Dimensional Probability)
TSH = Testing Statistical Hypotheses (Lehmann and Romano)
TPE = Theory of Point Estimation (Lehmann)
ELST = Elements of Large Sample Theory (Lehmann)
GE = Gaussian estimation: Sequence and wavelet models (Johnstone)
Additional Notes
| Topic | Link |
| Arzela-Ascoli Theorem | pdf |
| VC Dimension | pdf |
| Rates of convergence and moduli of continuity | pdf |
| Asymptotics for non-differentiable losses | pdf |
| Contiguity and asymptotics | pdf
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Scribing
The scribe notes should be written in prose English, as if in a
textbook, so that someone who did not attend the class will understand
the material. Please do your best, as it is good practice for
communicating with others when you write research papers.
The scribing schedule will be online soon.
All tex files and scribe notes from 2017, 2018, and 2019 are available
from their respective syllabi (2017,
2018, 2019). You can
download the LaTeX template and
style file for scribing lecture notes.
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